Probability - How does it work?!

But surely in the case of only 100 tosses (fnarr) 100 heads in a row would mean a coin that'd been tampered with?

No need for coin tampering, in fact no need for coins at all, as a purely mental exercise you can see how a heads > heads > heads > heads > heads > heads > heads > (etc) outcome is as likely as any other.

Shouldn't it even itself out to 50/50 over the full 100?

No, there is nothing pushing the system to 'even itself out'.

Whereby 50 heads in a row is equally likely as 50 tails in a row, or heads-tails-heads-tails-heads-tails etc or any other combo as you say?

Yep, all combinations are equally likely.